Questions about default class functions in Python

Question

Consider the following example of an iterative class which makes factorials from a given number:

import math

class Factorial(object):
  def __init__(self, num, maxsize=10e12):
    self.num = num
    self.maxsize = maxsize
  def __repr__(self):
    if __name__ == '__main__':
      return f'<{self.__class__.__name__} object at {hex(id(self.__class__))}>'
    else:
      return '<' + self.__class__.__module__ + '.' + self.__class__.__name__ + ' object at ' + hex(id(self.__class__)) + '>'
  def __iter__(self):
    for i in range(1,self.num+1):
      if math.factorial(i) > self.maxsize:
        break
      yield math.factorial(i)

So, of course we have the methods __init__, __repr__, and __iter__, which I have all read about online. I have two questions:

What would you call these methods? I know you can describe __init__ as a sort of constructor, but is there a special name that all of those __<blah>__ methods fall under when it comes to classes?
Is there a list of all of these so-called "special" or "built-in" class functions that tells what they are and what they do in a class context? The ones I already know of are __init__, __enter__, __next__, __exit__, __iter__, __str__, __repr__, and __call__. Or is this pretty much a complete list, except for a few?

I've been scratching my head about this for a while now (mostly because I don't know what to call these functions so I can't really research them).

I don't think there is an "official" name, but most people call them magic methods (which I personally don't like), special methods, or datamodel methods. I like that one, because searching for that term will bring up the Data Model page of the documentation, which describes most of those methods. — Patrick Haugh
– Patrick Haugh, Commented Nov 23, 2018 at 16:55
@PatrickHaugh Would it be under the "Special method names" list? That's what it appears to be. — moltarze
– moltarze, Commented Nov 23, 2018 at 16:56
The docs call them special methods. As Patrick says, they're often called magic methods. Another name is dunder methods — PM 2Ring
– PM 2Ring, Commented Nov 23, 2018 at 16:57
Thank you! Is there possibly a simpler guide to the special methods? — moltarze
– moltarze, Commented Nov 23, 2018 at 16:59
I've heard of them referred to as magic methods. rszalski.github.io/magicmethods — OrderAndChaos
– OrderAndChaos, Commented Nov 23, 2018 at 16:59

Blckknght · Accepted Answer · 2019-05-03 19:14:26Z

Since there's no answer to this reasonable question, I'll summarize the suggestions given in the comments as a community wiki.

The official Python documentation mostly calls methods like __init__ and __iter__ "special methods." It has a list of them in its chapter on the Python data model.

Python programmers often uses the less formal term "magic methods". Or, since the names are surrounded by double-underscores, the term "dunder method" may make sense, especially when you're going to need to be speaking their names out loud (you can say "dunder init" as a simple and clear way to express the name __init__ without tying your tongue in knots, an approach popularized by Ned Batchelder).

It's worth noting that some objects have special attributes that are not actually methods. For example, functions and modules have a __name__ attribute that is a string. (The module's __name__ is usable as a global variable within the module, and you'll often see used that way in if __name__ == "__main__" boilerplate.) All objects should have a __class__ attribute (which is a reference to their type), and many will have a __dict__ attribute (a dictionary) as well.

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